For digitalisation purposes i wrote little C program for STM32F303. I had devboard with this IC laying aroung and it incorporates impressive set of analog functions so it was no-brainer. This program oversamples ADC input to get higher resolution data and streams filtered data through USB-CDC interface which is interpreted by serialplot. Here is live video which shows that it is not a fluke - mechanical stress indeed influences substantially voltage offset!

At first glance data looks very promising! Huge voltage variations are seen when IC is stressed, but long-term data capture shows some flaws of this appriach to building weight scale. Both channels of op amps are closly tracking each other voltage, but mean value between them and calculated values separately drifts noticeably over time. Readings below were captured with load of 253g over 5mins:

And here are measurements without load:

Close resemblance between both channels can be seen and if noise is accumulated then channels would not track themself. So my guess is that temperature is culprit here as both ic's are close to each other so their temperature should be almost identical. Oven stabilisation may be a little overkill for this purpose, i hoped that offset drift would be symmetrical as opamps are glued in opposite directions but it is not the case - maybe different channels have transistors oriented in such way that it would produce reversed signal?